In the first Austin Powers movie, Dr. Evil steals a 50 kiloton nuclear weapon, straps it to a drill and is going to fire it into the mantle to trigger volcanic eruptions world wide.
My instinct is that, compared to a lot of nuclear weapons in the megaton range, 50 kilotons is not really a lot, and using it to try to move rock (even molten rock) is not going to accomplish his goal. Would it even cause a measurable change in the pressure that far down?
While a lot of posts have touched on the size of the explosion, the real impossible part is getting to the mantle. It was only fairly recently done by digging in the ocean where the mantle was pushed up more than normal.